A342902 a(n) is the smallest number that is the sum of n positive cubes in two ways.

1729, 251, 219, 157, 158, 131, 132, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126

Offset

2,1

Comments

This is r(n,3,2) in Alter's notation.

Links

Table of n, a(n) for n=2..63.

R. Alter, Computations and generalizations on a remark of Ramanujan, pp. 182-196 of "Analytic Number Theory (Philadelphia, 1980)", ed. M. I. Knopp, Lect. Notes Math., Vol. 899, 1981. See Table 2, page 190.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = n+63 for n >= 9.

G.f.: x^2*(1729 - 3207*x + 1446*x^2 - 30*x^3 + 63*x^4 - 28*x^5 + 28*x^6 - 61*x^7 + 61*x^8)/(1 - 2*x + x^2). - Charles R Greathouse IV, May 15 2026

Example

a(2) = 1729 = 12^3 + 1^3 = 10^3 + 9^3 (the famous Hardy-Ramanujan number).
a(3) = 251 = 5^3 + 5^3 + 1^3 = 6^3 + 3^3 + 2^3.

Prog

(PARI) a(n)=if(n>8, n+63, [1729, 251, 219, 157, 158, 131, 132][n-1]) \\ Charles R Greathouse IV, May 15 2026

Crossrefs

Cf. A001235, A011541, A230563, A342903, A343077, A343078, A343079, A343081, A343085.

Sequence in context: A344744 A013864 A394230 * A112140 A374417 A044883

Adjacent sequences: A342899 A342900 A342901 * A342903 A342904 A342905

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 03 2021

Status

approved